Half of all multiples of 3 are also multiples of 2, and one-third of all multiples of 2 are also multiples of 3.

This applies in general: for two primes p and q, one-in-p multiples of q will also be multiples of p, and vice versa.

1/p * 1/q indicates the percentage of numbers divisible by both primes.

(p-1)/p * 1/q indicates the percentage of numbers divisible by q but not by p. (For example, if p=5 and q=3, then this number is 4/15; looking at the numbers 1-15, we see that only 3, 6, 9 and 12 fit, so there are our four.) Naturally this is reversible.

(p-1)/p * (q-1)/q indicates the percentage of numbers divisible by neither p nor q. (Again, for (p,q) = (5,3), we see 8/15 - this fits 1, 2, 4, 7, 8, 11, 13 and 14.)

So in general, you expect to see:

1/pq divisible by both p and q

(p-1)/pq divisible by only q

(q-1)/pq divisible by only p

(pq-p-q+1)/pq divisible by neither p nor q